Thermodynamic Cycles

1
Thermodynamic Cycles
2
Review Thermodynamic Process
P
3
4
1
2
T

• Thermodynamic processes can be connected together
  to form a cycle (connect the dots)
• Corners represent the thermodynamic states of the
  system
• When the processes form a closed figure, its
  called a cycle

3
Cycles

• A diagram can be drawn with any pair of
  properties
• P-T
• P-V (allows the net work of a cycle to be
  determined Wintegral of pdV
• T-S (gives the net heat of a cycle recall 2nd
  law which states ds?dQ/T -gt Qintegral of Tds!
• If you can convert some of the heat to work, you
  have an engine!

4
Cycle Types

• Premixed Charge Otto Cycle, gasoline,
  spark-ignition engine
• Non-premixed charge or stratified charge engine
• (compression ignition or Deisel cycles)
• Gas Turbines Brayton Cycle
• Other cycles Rankine,

5
Where to start Air (ideal gas) cycles

• Assume no changes in gas properties (cp, MW, g,
  ) due to changes in composition, temp., called
  the IDEAL air cycle!

• REAL cycles must consider fuel-air mixture
• which is compressed, burned, expanded,
• with accompanying changes in thermodynamic
• properties

6
Premixed Charge Otto Cycle
Expand
4
P
s
v
5
Burn Constant Volume
3
Blowdown
v
s
1
2, 6
V (cylinder volume)
Compress
7
Otto Cycle
8
Thermal efficiency

• hthwhat you get/what you pay for

9
Thermal efficiency

• After some algebra

• independent of heat input
• efficiency increases as rc increases
• why not go to rc -gt ?
• why not?
• geometrical limitations, heat loss,
  irreversibilities
• (high compression -gt high T -gt high heat
  loss), knock

10
Thermal efficiency

• Example Auto engine rc8 g1.3
• hth0.46 (theoretical) hth0.30 at best (expt)
• Differences
• Heat Loss to valves, cylinder walls
• Incomplete combustion
• Friction
• Blow by, valves leak
• Throttling (Pexhaust ?Pintake)

11
Diesel Cycle
Combustion

• Stratified charge engine
• fuel injected after air compressed
• heat release doesnt occur instantly
• since fuel will take more time to
• burn than in the premixed case.
• This is bec. fuel must mix,
• vaporize, than burn. Takes time.
• To model this, combustion process
• assumed to occur at increasing
• volume, constant pressure

3
2
Expansion
P
4
Compression
6
1,5
V
New ratio V3/V2 introduced
12
Diesel Cycle
Define depends on the heat input
can show
gt1 for bgt1
thus
and
when b1
13
Ideal Brayton Cycle (Gas Turbines)

• Isentropic Compression (1-gt2)
• Constant pressure heat addition (2-gt3)
• Isentropic expansion (3-gt4)
• Constant pressure heat rejection (4-gt1)

P
3
2
4
1
V
14
Ideal Brayton Cycle
Heat Added
3
P
Expansion
3
2
T
s
v
2
4
Compression
s
4
v
1
1
Heat Rejected
s
V
15
Ideal Brayton Cycle
Wnet Wt Wc
where PR
Note